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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 342720.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 342720.bp1 | 342720bp1 | \([0, 0, 0, -171354648, 863500557278]\) | \(-11926249134908509075308544/2246680441062421875\) | \(-104821122658208355000000\) | \([]\) | \(48384000\) | \(3.4188\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 342720.bp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 342720.bp do not have complex multiplication.Modular form 342720.2.a.bp
sage: E.q_eigenform(10)